The tone is becoming increasingly optimistic as the two countries approach a USA deadline to reach a deal by Friday, when President Donald Trump plans to notify Congress that he'll sign a pact to replace the 24-year-old NAFTA.
Mnuchin made the comments a day after US President Donald Trump said that now was "not the right time to talk" to China, and that the US and Mexico had reached an agreement to revise Nafta, the three-nation pact that also includes Canada.
Canadian Prime Minister Justin Trudeau said Wednesday that while a new trade agreement with the USA and Mexico could be reached by Friday, Canada will not sign it if it is not in the country's best interests.
Freeland, who later met with Mexican officials on Tuesday evening, said she is due to dig into detailed discussions with Lighthizer on Wednesday.
"I think Canada very much wants to make the deal", he said, while again raising the possibility of a separate, bilateral deal with Mexico.
The president is critical of Canada's lopsided treatment of the US, especially with the northern nation's tariffs on dairy products that be almost 300 percent.
"The U.S. went from a $1.6 billion goods trade surplus with Mexico to a $70 billion goods trade deficit during that same time period", it added.
NAFTA is blamed for hastening the demise of US manufacturing as automakers and other manufacturers moved factories south of the Rio Grande. She said she was "encouraged" and "optimistic" upon her departure from the morning meeting, but she did not provide details.
"Our officials are meeting now, and we'll be meeting until very late in the night", Canada's Foreign Minister Chrystia Freeland told reporters Wednesday.
Guajardo said if Ottawa and Washington fail to come to agreement, Mexico would have to return to the negotiating table to revisit some of the auto industry rules.
Mexico's peso strengthened against the U.S. dollar, as did the Canadian dollar, while the United States dollar index weakened slightly.
Talks between Canada and the United States are intensifying as the two countries push to hammer out a deal on a revamped North American Free Trade Agreement by a Friday deadline, with both sides upbeat about the progress made so far.
Does Canada have to sign on, too? Otherwise the deal would need 60 votes, meaning multiple Democrats would have to support it. But they're hoping now Trump will reach an agreement with Canada.
That said, getting a new deal in place with Mexico in concert with the expected approval by Canada is viewed positively by automakers. US stocks edged to record highs for a third consecutive session.
The U.S.is seeking more market access for its milk products to the protected Canadian market.
Canada's dairy farmers operate under a protectionist system that manages supplies and prices, and imposes high tariffs to limit imports. At one point, Trump mused that simply imposing punishing tariffs on Canadian cars would be easier.
"We just said look, if you don't do something about these barriers that you have and these tremendous tariffs that you have for our farmers and others, then we're not going to be making a deal, we're just going to tariff you coming back in". Congress has to approve it.